The Economic and Welfare Effects of Tax-deferred Employer. Pensions in China

Transcription

1 The Economic and Welfare Effecs of Tax-deferred Employer Pensions in China Chunhong Zhao Cenral Universiy of Finance and Economics,China Absrac Based on he employer pension sysem and ax-deferred policy in China, his paper builds a general equilibrium model of overlapping generaions o analyze how he changes of employee conribuion and employer maching will affec he economic variables, such as he capial per worker, reurn rae o savings, wage, savings, consumpion and oal welfare, under hree fuure ax assumpions, namely ax rae in reiremen period is he same as, higher or lower han ha in working period. The research resuls are as follows: he effecs of he ax-deferred policy are up o he fuure ax rends o a large exen, we can hardly increase he reiremen consumpion and oal welfare a he same ime, he decrease of he welfare always follows he increase of he reiremen consumpion when he fuure ax rae falls, he employer maching affecs economic variables way more han employee conribuion does. Keywords: Employer pensions Tax rend Economic effecs OLG

2 . Inroducion The aging problem is no unique o some individual counry, i has become he global challenge we all have o face in he s cenury, he falling birh rae and longeviy risk are making hings worse in China. As he world s mos populous counry wih nearly one-fifh of he world populaion, solving he problem of supporing he old properly, China will conribue a lo o ackling global aging. There are hree pillars in China s old-age securiy sysem. The firs pillar is he social securiy sysem which is aimed o guaranee he minimum living sandards of he elderly. The second pillar is he supplemenary pension insurance se up by he employer, and i is o improve people s living sandards afer reiremen, which is also he research subjec in his paper. The hird pillar, he individual savings, is oally up o personal siuaions. The social securiy sysem almos covers all Chinese ciizens now, and afer decades of developmen, i has been making is way o successfully playing is role. While he second pillar is a recen inroduced program which calls for rapid growh o fulfill is mission o mee people s increasing consumpion need afer reiremen. Therefore, he China s Minisry of Finance, Human Resource and Social Securiy Deparmen and he Sae Adminisraion of Taxaion published: The Noice abou Some Issues Relaed o Individual Income Tax on Employer Pension and Occupaional Pension ( The Noice for shor). Which saes he deails, such as employee conribuion limi is 4% of one s average monhly pay for he previous year, abou China s employer pension ransferring from TEE o EET (T sands for axed and E for exemped). And he EET has been officially pu ino pracice since January, 04. The ax-favored Individual Reiremen Accouns were firs inroduced in 974 and he 40(k) plans in 978 in he U.S., boh of which were se up o encourage individuals wihou access o a pension or employees o save more in working period. In he meanime, he increasing naional savings migh have a good effec on domesic capial accumulaion and produciviy growh. Ever since he ax-favored plans came ino operaion, a lo of scholars have conduced a series of researches on hem. The 40(k) plans surely did a grea job and accumulaed a large amoun of money even hough he scienific research resuls on he effecs of he ax-favored plans differ from each oher. Wheher he ax-deferred employer pensions will work as i did in he U.S. is sill a quesion which need furher invesigaion, since here are a lo of differences beween China and America. The IRAs and 40(k) plans were o simulae individual savings because of he declining personal savings rae in he U.S., while in China, he naional savings rae is up o 50%, of which he governmen and corporae savings accouns for 30%. Besides, companies in China possess excess profis due o he imperfec compeiion marke. Therefore, any ax-deferred policy on employer pensions should designed o raise employer maching. A lo of lieraures have focused on ax-deferred privae pensions. Direr (00) buil a one working period and muliple reiremen periods model, and concluded ha i is possible o address he adverse selecion problem by axing annuiies purchased by high incomes and subsidizing annuiies purchased by low incomes. Amromin, Huang and Sialm (007) showed, under some condiions, ha here is a ax arbirage beween reducing morgage prepaymens and increaseing ax-deferred accoun conribuions. Bu Rydqvis, Schwarz and Spizman (04) hough ha he ax benefi of income smoohing hrough he privae reiremen sysem, namely o conribue o a

3 privae pension accoun when marginal ax raes are high and wihdraw when marginal raes are low, is negligible. Besides, quie a number of scholars have conduced research abou he effecs of ax-deferred accouns on savings. Poerb, Veni and Wise (995) poined ou ha hey found lile evidence ha 40(k) conribuions crowd ou oher forms of personal savings. Benjamin (003) esimaed ha abou one quarer of 40(k) balances represen curren ax he governmen abandoned, one quarer represen new naional savings, one quarer ransfer from he DB or DC plan and one quarer come from oher forms of family asses. Aanasio and DeLeire (00), Gomes, Michaelides and Polkovnichenko (009) all held ha ax-deferred accouns can help o promoe wealh accumulaion, bu have lile effec on increasing ne savings. Apar from he lieraures menioned above, here are sill many scholars sudied he effec of employer maching, such as Engelhard and Kumar (007), Zhou (009). Engelhard and Kumar concluded ha he worker paricipaion will increase by 5% and he balance of he 40(k) accoun will increase $365 a he same ime, if he employer maching increases 5 cens per dollar of employee conribuion. Overall, he research shows ha he 40(k) saving s elasiciy of employer maching is quie low, which means ha employer maching is really a poor insrumen wih which o increase saving for reiremen. Zhou found ha a ypical employer maching program may increase conribuion raes of low-income employees, and i increases he conribuion raes and he paricipaion raes of young employees a he same ime, bu i decreases conribuion raes of old employees and high-income employees. Mos imporanly, Creedy and Gues (008) sudied he macroeconomic effecs of he changes of he axaion of privae pensions in Ausralia, hey analyzed how he unexpeced changes of axaion of privae pensions will affec consumpion, savings, labor supply and social welfare under differen pension ax mode, and hey poined ou ha he more he conribuion, he greaer he influence of ax delay on savings, labor supply and social welfare, hough i may no change he form of he influence. Surely he ax-deferred policy and economic environmens in Ausralia are oally differen from ha in China. The hisory of employer pensions jus sared in 005, mos lieraures on employer pensions in China have been focusing on he paerns of he employer pensions (Deng, 004), he obsacle and counermeasures for he employer pensions o develop (Zhao, 007). There are no lieraures ha quaniaively analyze he economic and welfare effecs of he ax-deferred employer pensions. Therefore i is of boh heoreical and pracical imporance for his paper o analyze he economic and welfare effecs of he ax-deferred employer pensions in China according o he newly inroduced ax policy. In his conex, his paper builds a general equilibrium model of overlapping generaions o analyze how he increase of employee conribuion, employer maching in working period will affec he social welfare and economic variables, such as capial per worker, ineres rae, wage, savings and reiremen consumpions, under hree differen marginal ax raes assumpions: ) ax rae in reiremen period is he same as ha in working period, ) ax rae in reiremen period is higher han ha in working period, 3) ax rae in reiremen period is lower han ha in working period. According o he las 30 years daa abou ax rae in China, he ax rae changes a lo, and mosly goes up. The uncerainy of some policy may influence anoher policy s effeciveness, someimes may be a oal offse. So his paper made a quaniaive analysis. The paper is organized as follows. Secion describes he model. Secion 3 presens calibraion of he model and 3

4 numerical resuls. Secion 4 shows policy implicaions and conclusion.. The Model The model in his paper is developed from Diamond (965), and i is a general equilibrium model of wo period overlapping generaions wih hree secors: households, firms and governmen, which are described in urn below. The social securiy was no aken ino accoun for simpliciy and ransparency, surely such a pracice is on one condiion ha leaving ou social securiy will no affec he research resuls of his paper. The key assumpion is ha each person s life has wo ime periods: youh and old age, and i is assumed ha only he young work; he old are reired. Here we use N, sands for he people who were born in period, namely he young people in working period, N, + sands for he reired people in period +, and n sands for he fixed populaion growh rae (we assume ha he populaion growh rae is he same as he labor growh rae in his paper), hen we have he following equaion N ( ) = + n N, and he oal,, + n amoun of people in period is given by N = N, + N, = N, + N, = N,. + n.. Households The young people who were born in period offer labor o ge pay, and hey ge heir disposable income afer conribuing o heir ax-deferred employer pension accouns and paying individual income ax (which also means he labor income ax, since we only ake labor income ax ino accoun in working period in his paper, and i will be explained below). Par of he disposable income was deposied and he res was consumed. In period +, he people who were born in period reire and consume wha hey saved in working period and wha hey ge from heir employer pension accouns. Households derive uiliy from consuming goods and hey choose consumpions in boh working period and reiremen period and savings o maximize heir lifeime uiliy. The household s ineremporal problem is as follows: c, c, + max { c, c, s,, } U = + + β () s.. c, = a τ, ( a) w s () ( ) ( τ ) c = + r s + A (3), + +, + + ( )( η ) A = + r a+ w (4) + + Where, c,, is he consumpion in working period, c, + is he consumpion in reiremen period and U is he lifeime uiliy. The consan relaive risk aversion coefficien > 0 and 4

5 , (0,) is he discoun facor of he fuure uiliy. The following parameers and β variables a, ητ,,,, τ, +, w, s, r+ represen respecively: he employee conribuion rae, he employer maching rae, he individual income ax rae for young people in period, he individual income ax rae for reired people in period +, he wage in period, he savings in period and he reurn rae o savings in period +. A + is he oal ax-deferred accoun balance. The firs order condiion of he household s ineremporal problem is: c + r +, + c, = β Which means ha consumpion when young equals o consumpion when old if he real reurn o savings is equal o he rae of ime discoun, ha is o say if he incenive o save for he fuure is sufficien o offse he discouning of fuure uiliy. (5).. Firms The firms produce oupu of a single good according o a Cobb-Douglas producion funcion. Oupu,Y, in period, is given by Y = AK N. Where A is an exogenous echnology α α, parameer, K is he capial sock in period,, N is he labor in period, and ( 0,) α is he share parameer of capial. Here is anoher expression of he producion funcion y = Ak α. Where, k, is capial per labor, and y is oupu per labor. The employer maching is a cerain percenage, η ( 0,), of he oal wage. According o Euler s heorem in producion, α α we have he following funcion ( η ) Y = AK N = r K + + w N. The opimal sock is,, deermined by he firs-order condiion ha he cos of he capial, r, is equal o he marginal produc of capial, and he price of labor, w, is equal o he marginal produc of labor: r Ak α = α (6) w = ( α ) + η Ak α (7).3. Governmen The balanced budge condiion for he governmen means ha a reducion in axaion on employer pension mus be accompanied by eiher reducing governmen spending, or raising he ax rae applying o oher kind of income, in his paper, we assume ha he reducion in axaion is 5

6 balanced by cuing governmen spending, and we only ake labor income ax ino accoun, as oher kinds of income ax don maer ha much in our analysis. The governmen spending is denoed as,g, and T is he oal governmen ax revenue. ( ) τ,, τ,, T = a wn + A N (8).4. The General Equilibrium soluion The capial sock in period + is formed by he accumulaion of he conribuion and employer maching in he pension accoun and he individual savings in period (see o appendix A). ( η ) ( ) + s + a+ w = + n k (9) Based on he iniial capial sock ( k 0 ) and he value of all parameers, he compeiive equilibrium of his economic sysem is a sequence, { c,, c, +, s, r+, w, A+, k+ } value of which in every period all saisfy he equaion from () o (9) above. Plunge equaion () o (4) and equaion (6), (7), (9) ino equaion (5), we can obain he dynamic general equilibrium sysem described by he difference equaion. α ( α ) ( ) ( a + )( ) τ, + η α α + Ak+ + n k+ Ak = + η α + α Ak + α α ( τ, + aτ, + η) Ak ( + n) k+ β + η Assume ha here is only one seady sae equilibrium soluion for he dynamic general equilibrium sysem, and we can ge he linear expression of equaion (0) hrough he firs order Taylor series expansion a seady sae: Where ( ) ( ) i k k j k k + = + 0 ( a )( ) ( + ) ( + n)( ) α + n α α α i ( n)( A k ) ( Ak α α α α ) ( αak = ) Ak + β β = 0, he (0) ( a )( ) ( α ),, ( α ) α, Ak ( Ak + + α ) + Ak + η τ + τ + η α α τ + η α α And η β α( α ) τ + aτ + η j = τ, + a + η + + αak Ak + αak + η β,, α ( ) ( α α ) ( ) 6

7 The seady-sae condiion for equaion (0) is k 0 + k j < = < k k i, namely i+ j < 0. We can derive from equaion (0) ha he capial per labor, k, a seady sae, saisfies he following equaion: α ( α ) ( ) ( a + )( ) τ, + η α α + Ak + n Ak = + η α α ( τ, + aτ, + η) Ak ( + n) β + η The share parameer of capial in producion funcion α, he consan relaive risk aversion coefficien, he discoun facor of he fuure uiliy β, he fixed populaion growh rae n, he employee conribuion rae a, he employer maching rae η, he individual income ax rae in working period τ,, he individual income ax rae for reired people in period +, +. All of he facors above deermine he capial per labor a seady sae ogeher. From equaion (), (3), (5), (6), and equaion (7), we can derive he opimal soluion for he economic variables a general equilibrium: τ () α α c = ( τ, + aτ, + η) Ak ( + n) k + η α ( α ) ( ) ( a + )( ) τ η α + η, + α c = + Ak + n k Ak ( ) ( a + η)( α) s = + n k Ak α + η () (3) (4) r α Ak α = (5) α w = Ak α + η (6) U c c = + β (7) 3. Numerical Simulaions 3.. Calibraion 7

8 The OLG model is calibraed o he Chinese economy wih ax-deferred employer pension accouns. The consan relaive risk aversion coefficien is se a.0 according o Blanchard, Fisher and Miyazao. Auerbach and Kolikoff (987) esimaed ha he one-year consumpion paience was 0.98, which was adoped by Zaigui Yang (008) oo, we assume ha he oal working period is 8 years in his paper, so he discoun facor of fuure uiliy is se a, n =, β =. The populaion growh rae is esimaed a, in according o he 03 China Saisical Yearbook. The oal facor produciviy, A, is se a.0. The share parameer of capial,α, is usually se a 0.30 in developed counries (Barro and Sala-I-Marin, 004. Pecchenino and Polland, 00). Since he price of labor in China is sill lower compared o developed counries, he share parameer of capial is se a 0.35 in his paper. According o The Noice, he individual conribuion (no more han 4% of one s average monhly pay for he previous year) is allowed o be deduced before paying individual income ax, so is he employer maching. Reurns on he ax-deferred accouns are exemped from he individual income ax oo, and he wihdrawal will be axed a ordinary income ax rae. The Employer Pension Pilo Scheme published in 004 saes ha he employer maching for he whole year is no more han one-welfh of he oal paymen for previous year, of which he sum of employee conribuion and employer maching is no more han one-sixh. So we assume ha he employer maching rae is 00% of conribuion, which is o say ha he employer maching is equal o employee conribuion, a = η = 3%. Wih he rapid developmen of Chinese economy, he average wage in China now is more han hiry imes higher han ha of hiry years ago, and he seven-level progressive marginal individual income ax rae is in use afer many aleraion of ax regime have been made. We can predic precisely where he economy in China will go, o wha level he wages will increase and how he ax rae will change in he fuure hiry years. So based on he curren wage level and ax rae, he labor income ax rae in working period τ, is se a 0%, and he individual income ax τ rae in reiremen period, + is se a 0%, 3% and 0% respecively. 3.. Numerical Resuls Here we give he specific simulaion resuls of how he changes of employee conribuion and employer maching will affec he economic variables, such as he capial per worker, ineres rae, wage, savings, consumpion and oal welfare The change of employee conribuion The following hree ables show how he economic variables will change wih he increase of employee conribuion, and E sands for he employee conribuion rae elasiciy of economic variable. The negaive E value means ha he economic variable decreases wih he increase of he 8

9 employee conribuion rae. Tab le The numerical resuls when ax rae is se a 0% in reiremen period a k r w c c s U % % % E 3.83% -.49%.34%.3% 0.0% -8.9% 0.9% Tab le The numerical resuls when ax rae is se a 3% in reiremen period a k r w c c s U % % % E.74% -.3% 0.6% 0.74% 0.3% -.67% 0.64% Tab le 3 The numerical resuls when ax rae is se a 0% in reiremen period a k r w c c s U % % % E 6.5% -4.4%.8%.58% -0.3% -4.8%.% ). Capial sock and facor price The capial per labor and wage will go up wih he increase of employee conribuion, while he reurn rae o savings decreases, whaever he ax rae in reiremen period will be. The main reason for he reurn rae o savings going down is he accumulaion of he capial sock. The wage is deermined by boh he capial per labor and employer maching rae, since he employer maching rae is se a a consan number, 3%, here, he rise of wage is almos compleely due o he increase of capial sock. Surely here are many differences among he hree ables above abou he change of capial sock and facor price when he ax rae in reiremen period differs. The capial per labor, reurn rae o savings and wage are more elasic o employee conribuion rae when ax rae in reiremen period is higher han ha in working period, ake capial per labor for example, he conribuion rae elasiciy of capial per labor is 6.5% when ax rae goes up in reiremen period, almos four imes as big as ha when ax rae decreases. There are several reasons o explain his, he main 9

10 reason is ha he higher ax rae in reiremen period adds up o he governmen ax revenue, which in urn increases he governmen savings and acceleraes he accumulaion of capial sock. ). Savings According o his paper, he employee conribuion does crowd ou personal savings. The hree ables above show us ha he crowd-ou effec is he larges when ax rae in reiremen period is se a 3%, and wo reasons should be menioned o accoun for his. On one hand, he subsiue effec which comes from he rise of he reurn rae o savings promoe he increase of savings, while on he oher hand, he income effec which comes from he decrease of ax rae in reiremen period should be responsible for he reducion of he savings. The oal effec is he decreasing savings, since he income effec dominaes he subsiue effec. 3). Consumpion and welfare The disposable income in working period decreases because of he increase of employee conribuion rae, bu he young prefer cuing down savings o reducing consumpion, so as o mainain or even increase heir consumpion level in working period. This is mosly because ha he decreasing reurn rae o savings makes i much less aracive o save. Generally speaking, he oal welfare goes up wih he increase of employee conribuion rae. Bu he welfare is lower when ax rae in reiremen period is 3% han ha when ax rae in reiremen period is se a 0%, he reason for his in as follows. The oal welfare is co-deermined by he consumpion in working period and ha in reiremen period, consumpion in working period is lower and consumpion in reiremen period is higher in able compared o hose in able, and he welfare gain from he increase of consumpion in reiremen period in less han he welfare loss from he reducion of consumpion in working period. The effec of he increase of employee conribuion rae on consumpion in reiremen period changes wih he fuure ax rae in reiremen period. The reiremen consumpion increases wih he rise of employee conribuion rae when he ax rae sands sill or goes down, namely when he ax rae in reiremen period is se a 0% or 3%. On he conrary, he reiremen consumpion decreases wih he rise of employee conribuion when ax rae in reiremen period goes up. In he meanime, employee conribuion rae elasiciy of reiremen consumpion in able is 3 imes as large as ha in able. Among he hree ables, he lower he ax rae in reiremen period, he more he reiremen consumpion when he employee conribuion rae is he same. The ax-deferred accouns effec on reiremen consumpion depends on where he fuure ax rae goes. The ax-deferred policy can promoe consumpion in reiremen period, if he inflaion in he fuure, resuling from he governmen easing moneary policy which is aimed a mainain high speed economic growh, confrons he reired wih much higher marginal ax rae, or if he governmen finances is increasing fuure spending by raising governmen ax revenue, which in urn booss he ax rae in reiremen period. Conrarily, he reiremen consumpion will increase a lo if he fuure ax rae goes down The change of employer maching 0

11 Here in his par we assume ha he employee conribuion rae is consan, 3%, while he employer maching rae is respecively 00%, 00% and 300% of conribuion. And E sands for he employer maching rae elasiciy of economic variable. The negaive E value means ha he economic variable decreases wih he increase of he employer maching rae. Tab le 4 The numerical resuls when ax rae is se a 0% in reiremen period η k r w c c s U 3% % % E 6.60% -4.9% -3.35%.94% 0.0% -4.85%.56% Tab le 5 The numerical resuls when ax rae is se a 3% in reiremen period η k r w c c s U 3% % % E 3.05% -.98% -4.60%.30% 0.40% -5.30%.% Tab le 6 The numerical resuls when ax rae is se a 0% in reiremen period η k r w c c s U 3% % % E 0.98% -7.4% -.8%.63% -0.55% -30.8%.00% The hree ables above vividly show ha he wage decreases wih he rise of employer maching rae, since he higher maching rae increase he corporae coss, which is quie he opposie of wha happens o he employee conribuion. Apar from wha menioned above, he employer maching has he same effec on economic variables as employee conribuion did, only o a greaer exen. Take capial per labor for example, when he ax rae in reiremen period is se a 0%, 3% and 0% respecively, he capial per labor increases by 3.83%,.74%, 6.5%, respecively if employee conribuion rae increases by %, and 6.60%, 3.05%, 0.98% when employer maching rae increases by %, which implies ha i s more effecive o increase employer maching when here is a posiive effec o do so. 4. Conclusion and Policy Implicaions

12 To summarize he simulaion resuls of how he changes of employee conribuion and employer maching will affec economic variables, a number of resuls are as follows. Firsly, he effecs of he ax-deferred policy are up o he fuure ax rends o a large exen. A ax-deferred policy can promoe consumpion in reiremen period, if he inflaion in he fuure, resuling from he governmen easing moneary policy which is aimed a mainain high speed economic growh, confrons he reired wih much higher marginal ax rae, or if he governmen finances is increasing fuure spending by raising governmen ax revenue, which in urn booss he ax rae in reiremen period. On he conrary, he reiremen consumpion will be simulaed largely by a ax-deferred policy if he ax rae in reiremen period is much lower han ha of working period. Bu he problem is ha we can predic he policy change in he fuure, besides, he opimal policy in he fuure which will be made according o he economic circumsance a ha ime is always no he bes for oday because of he Time Inconsisency. Secondly, we can hardly increase he reiremen consumpion and welfare a he same ime, he decrease of he welfare always follows he increase of he reiremen consumpion when he fuure ax rae falls. The welfare is deermined by consumpion boh in working period and reiremen period. One uni of consumpion in working period brings more welfare han ha in reiremen period because of ime preference and ime value of money. The difference of ime preference implies he differen proporion of reiremen consumpion in oal welfare, he subjecive discoun facor, deermined by ime preference, is an imporan facor in deciding he oal welfare, which also can parly explain he conradicion beween increasing reiremen consumpion and raising welfare. Surely he imperfecion of policy is objecive which can hardly be avoided, and his calls for he decision maker o make a choice. Thirdly, he employer maching affecs economic variables way more han employee conribuion does. The increase of employer maching is much more effecive in raising consumpion and welfare han he increase of employee conribuion, which is because of he income increase resuling from employer maching increase. Wha s worh o be menioned is ha employer maching increase is superior o conribuion increase in accumulaing capial and cuing down reurn rae o savings oo. Some policy implicaions arise from he sudy of he simulaion resuls. Firs, a ax deducion policy, namely EEE, is advisable in his paper, which means he conribuion and employer maching is deduced from he axable income, and his is exacly wha s being adoped in Hungary. Employees are immune o ax change in he fuure wih a ax-deduced accoun, which is o say ha employee can ge a definie benefi from a ax-deduced accoun whaever he fuure ax rend and ax policy will be, and his in urn makes employee much more inclined o conribue o he ax-deduced accoun. The employee s ax burden is sill prey high in China according o Annual Repor 0 by he Word Bank, and a ax-deduced accoun will conribue o lower he ax-burden. Second, o increase employer maching is preferable. On one hand, economic variables, such as savings and ineres rae, are more sensiive o employer maching, and China is now going hrough he iniial sage of ineres rae liberalizaion, he lower ineres rae, resuling from he increase of employer maching, will give more liquidiy o moneary marke. On he oher hand, he increase of employer maching is able o increase consumpions in boh periods and reduce savings a same ime, which migh be an advisable soluion o he dilemma of high savings and inadequae consumpion in China.

13 I s imporan o noe ha he resuls in his paper hold up subjecing o all he qualificaions menioned above, and some facors such as he difference among households, he uiliy of leisure, expecaion and moraliy will be aken ino accoun in our fuure work. Appendix A The naional income ideniy is given by: Y = C + I + G Y = rk + + η wn Where ( ), C = c N + c N,,,, I = K = K K + + ( ) ( )( ) G = T = a τ wn + a+ η + r τ w N,,,, ( ) c = a τ a w s,, ( ) ( η)( )( τ ) c = + r s + a+ + r w,, Plunge he equaion above o he naional income ideniy gives: Divided by, N, ( η) ( ) ( η)( ) K = a+ wn + rk + s N + r s N a+ + r w N +,,,,, we have he following equaion: r n k s a w + n k s a w + + n z = + n k s a+ η w, hen: ( + ) ( + η) = ( + ) ( + η) If we se, ( ) ( ) z + + r = z + n The equilibrium condiion for seady soluion is ha, z + = 0, which means: ( η ) ( ) + s + a+ w = + n k References Amromin, Gene, Huang, Jennifer, Sialm, Clemens, 007. The radeoff beween morgage prepaymens and ax-deferred reiremen savings. Journal of Public Economics 9, Aanasio, Orazio P., DeLeire, Thomas, 00. The effec of individual reiremen accoun on household consumpion and naional saving. The Economic Journal,

14 Benjamin, Daniel J., 003. Does 40(k) eligibiliy increase saving? Evidence from propensiy score subclassificaion. Journal of Public Economics 87, Creedy, John, Gues, Ross, 008. Changes in he axaion of privae pensions: Macroeconomic and welfare effecs. Journal of Policy Modeling 30, Direr, A., 00. The axaion of life annuiies under adverse selecion. Journal of Public Economics 94, Engelhard, Gary V., Kumar, Anil, 007. Employer maching and 40(k) saving: evidence from he Healh and Reiremen Sudy. Journal of Public Economics 9, Gomes, Francisco, Michaelides, Alexander, Polkovnichenko, Valery, 009. Opimal savings wih axable and ax-deferred accouns. Review of Economic Dynamics, Kingson, Geoffrey, Piggo, John, 993. A Ricardian Equivalence Theorem on he axaion of pension funds. Economics Leers 4, Liu, Zilan, 004. Sudies on he Choice of Occupaion Pension Scheme. Quaniaive and Technical Economics (3), Pecchenino,R.,P. Pollard, 00. Dependen Children and Aged Parens:Funding Educaion and Social Securiy in an Aging Economy. Journal of Macroeconomics 4, Poerba, James M., Veni, Seven F., Wise, David A., 995. Do 40(K) conribuions crowd ou oher personal saving? Journal of Public Economics 58, 3. Rydqvis, Krisian, Schwarz, Seven T. Spizman, Joshua D., 04. The ax benefi of income smoohing. Journal of Banking & Finance 38, Samuelson, Paul A., 958. An Exac Consumpion-Loan Model of Ineres wih or wihou he Social Conrivance of Money. Journal of Poliical Economy66, Wang Xiaofang, Zhai Yonghui, Yan Haifeng, 00. Economic Effecs of he Occupaional Pension Sysem: he Research based on General Equilibrium Model. Nan Kai Economic Sudies 5, Yang, Zaigui, 008. The Public Pension for Enerprise Employees, Benefi Replacemen Rae and Populaion Growh Rae. Saisical Research 5(5), Zhao, Feifei, 007. The Obsacles and Counermeasures o Promoe Occupaion Pension in China. Science & Technology Associaion Forum, Zhou, Jie, 009. The effecs of employer maching and income risk in 40(k) plans. Economic Modelling 6,